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Jerusalem Bike Lane Analysis - Methodology

Overview

This tool ranks proposed ("wishing list") bike lanes by their potential contribution to city-wide accessibility. It uses a gravity-based accessibility model to measure how well people can reach jobs across the city, with bike lanes significantly reducing the effective travel cost.

The Accessibility Model

Core Formula

N = Σ_i Σ_j P_i × E_j × τ_ij^θ

Where:

• P_i = Population of area i (potential trip origins)
• E_j = Employment in area j (potential trip destinations)
• τ_ij = Travel cost (shortest path distance in km) from area i to area j
• θ = Distance decay parameter (negative, typically -1 to -2)

Parameters

K - No-Lane Penalty

Roads without bike lanes are penalized by multiplying their length by K:

• weight = length for roads WITH bike lanes
• weight = length × K for roads WITHOUT bike lanes

Higher K values mean cyclists strongly prefer bike lanes: K=10 (mild), K=100 (strong, default), K=500 (very strong).

θ (Theta) - Distance Decay

Controls how quickly accessibility decreases with distance:

• θ = -0.5: Slow decay (long trips acceptable)
• θ = -1.0: Moderate decay (default)
• θ = -2.0: Fast decay (only nearby destinations matter)

References:
Donaldson, D., & Hornbeck, R. (2016). Railroads and American economic growth: A "market access" approach. The Quarterly Journal of Economics, 131(2), 799-858.
Tsivanidis, N. (2024). Evaluating the Impact of Urban Transit Infrastructure: Evidence from Bogotá's TransMilenio. American Economic Review, 116(2), 418-463.

Data Sources

Data	Source	Year
Statistical Areas	Jerusalem Transportation Master Plan Team	2025 projections
Population (pop_2025)	Jerusalem Transportation Master Plan Team	2025 projections
Employment (emp_2025)	Jerusalem Transportation Master Plan Team	2025 projections
Completed Bike Lanes	Jerusalem Transportation Master Plan Team	Current
Under Construction Bike Lanes	Jerusalem Transportation Master Plan Team	Current
Wishing List Bike Lanes	The author	Proposed
Road Network	OpenStreetMap	Current

Road Network Construction

The road network is built from Jerusalem road data (from OpenStreetMap, KML format) with the following process:

1. Node Creation: Road endpoints are snapped to a grid (15m tolerance) to create a connected graph
2. Edge Creation: Each road segment becomes an edge with its physical length as the base weight
3. Bike Lane Matching: Existing bike lanes are spatially matched to road edges using a 15m buffer and 50% overlap threshold
4. Coordinate Systems: Calculations use Israeli TM (EPSG:2039) for accurate distance; display uses WGS84 (EPSG:4326)

Network Connectivity

The tool ensures the network is fully connected through several mechanisms:

Node Merging

• Tolerance: Nodes within 15 meters are merged into a single node
• Purpose: Handles imprecise GPS coordinates and ensures lane endpoints connect properly to roads

Intersection Detection

• Bike lanes are overlaid on the road network
• Intersection points between bike lanes and roads are detected automatically
• New nodes are created at every intersection point
• Edges are split at intersection points to enable routing through the network

Gap Connection Algorithm

For bike lanes with gaps between segments:

1. Endpoint Extraction: Extract start and end points from all lane geometries
2. KD-Tree Indexing: Build spatial index for efficient nearest-neighbor queries
3. Dangling Endpoint Detection: Identify endpoints not touching other lanes (within 1m tolerance)
4. Gap Bridging: Connect dangling endpoints to nearest neighbor within 50m tolerance

Component Connection

For disconnected network components:

1. Component Detection: Find all connected components using graph algorithms
2. Minimum Spanning Tree Approach: Connect isolated components by adding edges between closest nodes

This connectivity fixing is essential because raw GIS data often has small gaps, coordinate mismatches, or isolated segments that would otherwise break shortest path calculations.

Shortest Path Algorithm

We use Dijkstra's algorithm to compute shortest paths between all area centroids:

• Graph: Undirected weighted graph where edge weight = length × K for roads without bike lanes
• Source: Nearest network node to each area centroid
• Output: Distance matrix τ_ij between all area pairs

Reference: Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269-271.

Online Computation

All accessibility calculations are performed in the browser using JavaScript:

1. Baseline Computation: When K or θ changes, compute accessibility with existing lanes only
2. Network Update: When wishing lanes are selected, mark their corresponding road edges as bike lanes (weight = length instead of length × K)
3. Full Recomputation: Run Dijkstra from each of the ~200 area centroids to compute new τ_ij matrix
4. Accessibility Aggregation: Sum P_i × E_j × τ_ij^θ for all pairs

How Lanes Are Ranked

1. Baseline Calculation: Compute total N using existing bike lanes only
2. With Selected Lanes: Add selected wishing lanes and recompute N
3. Improvement: %Δ = 100 × (N_new - N_baseline) / N_baseline

Area Accessibility

Origin Accessibility (where people live):

acc_origin[i] = Σ_j E_j × τ_ij^θ

Measures how many jobs area i residents can access (weighted by distance).

Destination Accessibility (where jobs are):

acc_dest[j] = Σ_i P_i × τ_ij^θ

Measures how many people can reach jobs in area j (weighted by distance).

Visualization

• Area Colors: Spectral colormap (blue → cyan → yellow → orange → red) with logarithmic scaling
• Accessibility Mode: Shows absolute accessibility values
• Change Mode: Shows percentage improvement from baseline after adding selected lanes